(8x+7)4x=13

Solution for (8x+7)4x=13 equation:

(8x+7)4x=13

We move all terms to the left:

(8x+7)4x-(13)=0

We multiply parentheses

32x^2+28x-13=0

a = 32; b = 28; c = -13;
Δ = b2-4ac
Δ = 282-4·32·(-13)
Δ = 2448
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2448}=\sqrt{144*17}=\sqrt{144}*\sqrt{17}=12\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-12\sqrt{17}}{2*32}=\frac{-28-12\sqrt{17}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+12\sqrt{17}}{2*32}=\frac{-28+12\sqrt{17}}{64}
$